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 A035884 Coordination sequence for diamond structure D^+_16. (Edges defined by l_1 norm = 1.) 1
 1, 0, 512, 0, 44032, 0, 1549824, 0, 30349312, 524288, 391784960, 26738688, 3702064128, 508035072, 27315850752, 5588385792, 164415418368, 42844291072, 834237682176, 253170810880, 3662806408192, 1226904698880, 14215186707968, 5082890895360, 49621579941888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf). FORMULA G.f.: (x^32 +496*x^30 +35960*x^28 +906192*x^26 +10551068*x^24 +524288*x^23 +68444400*x^22 +18350080*x^21 +285430600*x^20 +143130624*x^19 +733841744*x^18 +374865920*x^17 +1022804550*x^16 +374865920*x^15 +733841744*x^14 +143130624*x^13 +285430600*x^12 +18350080*x^11 +68444400*x^10 +524288*x^9 +10551068*x^8 +906192*x^6 +35960*x^4 +496*x^2 +1) / ((x-1)^16*(x+1)^16). - Colin Barker, Feb 26 2013 MAPLE f := proc(m) local k, t1; t1 := 2^(n-1)*binomial((n+2*m)/2-1, n-1); if m mod 2 = 0 then t1 := t1+add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n); fi; t1; end; where n=16. MATHEMATICA CoefficientList[Series[(x^32 + 496 x^30 + 35960 x^28 + 906192 x^26 + 10551068 x^24 + 524288 x^23 + 68444400 x^22 + 18350080 x^21 + 285430600 x^20 + 143130624 x^19 + 733841744 x^18 + 374865920 x^17 + 1022804550 x^16 + 374865920 x^15 + 733841744 x^14 + 143130624 x^13 + 285430600 x^12 + 18350080 x^11 + 68444400 x^10 + 524288 x^9 + 10551068 x^8 + 906192 x^6 + 35960 x^4 + 496 x^2 + 1)/((x - 1)^16 (x + 1)^16), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *) CROSSREFS Sequence in context: A217915 A263167 A139303 * A035596 A095843 A095882 Adjacent sequences:  A035881 A035882 A035883 * A035885 A035886 A035887 KEYWORD nonn,easy AUTHOR Joan Serra-Sagrista (jserra(AT)ccd.uab.es) EXTENSIONS Recomputed by N. J. A. Sloane, Nov 27 1998 More terms from Colin Barker, Feb 26 2013 STATUS approved

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Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)